Analysis of variance in complex experimental designs:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
San Francisco, Calif.
Freeman
1974
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 352 S. graph. Darst. |
| ISBN: | 0716707748 |
Staff View
MARC
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| 100 | 1 | |a Lindman, Harold R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Analysis of variance in complex experimental designs |c Harold R. Lindman |
| 264 | 1 | |a San Francisco, Calif. |b Freeman |c 1974 | |
| 300 | |a X, 352 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Analyse de variance | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xi
1 Review of Statistical Concepts 1
Probability Theory 1 Mathematical Concepts of
Probability 1 Applied Probability Theory 2
Distribution Theory 3 Joint Distributions 4
Summary Values 4 Covariance and Correlation 6
Sampling 7 Point Estimation 7 Hypothesis
Testing 8 Power 9
Summation 9
Notation 10
2 Important Distributions 12
The Normal Distribution 12
Distributional Notation 13
Chi Square 14
Noncentral Chi Square 15
t Distribution 16
F Distribution 17
Noncentral F 17
Tables and Interpolation 18
vi Contents
3 Analysis of Variance: One way, Fixed
Effects 20
Assumptions 20
Analysis: Equal Sample Sizes 22 Mean Square
Within 23 Mean Square Between 24 Mean
Square Total 25 The F Test 26 Expected
Values of Mean Square Within and Between 27
Robustness of F 31 Effects of Nonnormality 31
Unequal Variances 32 Independence of
Observations 35
Power of the F Test 36
Computational Formulas 37
Analysis; Unequal Sample Sizes 39 Computational
Formulas 42 Power of F with Unequal Sample
Sizes 42 Robustness of F with Unequal Sample
Sizes 43
Other Possible F Tests 44
Exercises 47
4 Comparing Groups 51
Proportion of Variance Accounted For 51
Graphs and Figures 54
Planned Comparisons 55 General Theory 57
Confidence Intervals for Planned Comparisons 60
Necessary Assumptions and Their Importance 60
Independent Hypotheses 63 Relationship to
Ordinary F 67 Interpreting Multiple Significance
Tests 70 Planned Comparisons and the Grand
Mean 71 yz for Planned Comparisons 72
Post Hoc Comparisons 73 Adjusted Significance
Levels 73 Fisher s Method 74 The Scheffe
Method 74 Relationships Between 5 and F 77
The T Method of Post Hoc Contrasts 77 Relationship
of the T Method to an Overall Test of Significance 78
Increasing the Power of Post Hoc Comparisons 79
Comparison of the S and T Methods 83 Critique of
the S and T Methods 83 Other Post Hoc Comparison
Methods 84 Confidence Intervals for Individual
Means 84
Exercises 84
Contents vii
5 Two way Analysis of Variance 88
Main Effects 88 The A Main Effect 89
The B Main Effect 89 Relationships to
Planned Comparisons 92
Interaction 92 The Model Equation 94
Interaction Mean Square 94 Interpreting
Interaction 97
Interpreting Main Effects 97
Simple Effects 98 Simple Tests on Means 99
Computational Formulas 100
Unequal Sample Sizes 100
Expected Mean Squares 102
Power of the Tests 104
Robustness of the Tests 104
Transformations on the Data 105
Pooling Sums of Squares 106
One Observation Per Cell 108
Exercises 108
6 Random Effects 112
One way Model 112 Model Equation and
Assumptions 113 Characteristics of Random
Effects 114 Mean Squares 115 Comparison
with the Fixed Effects Mode! 116 The F Test 117
Importance of Assumptions 119 Hypotheses about
the Grand Mean 120
Two way Model 121 The Model and the
Assumptions 124 Expected Mean Squares and
F Ratios 127 Note on Terminology 133
Robustness 133 Variance Estimates 134 Power
Calculations 135 Pooling Sums of Squares 135
Planned and Post Hoc Comparisons 136 Contrasts
136
Exercises 138
7 Higher way Designs 143
Kinds of Models 147
Assumptions 147
Mean Squares 149 Rules for Calculating Sums of
Mean Squares 149 Rules for Calculating Degrees
viii Contents
of Freedom and Mean Squares 151
Expected Mean Squares 151
F Ratios and Variance Estimates 154 Pooling Sums
of Squares 154 One Observation per Cell 155
Quasi F Ratios 155 Box s Correction 156
Comparisons 156 Standard Method 156
Analyzing Planned Comparisons 160 Approximate
Planned Comparisons 162 Exact Planned
Comparisons —Special Cases 163
Exercises 164
8 Nested Designs 166
Two way Model 168 Sums of Squares and Degrees
of Freedom 170 Models 171 Assumptions
173
Higher way Models 173 The Model Equations
176 Sums of Squares and Degrees of Freedom 178
Expected Mean Squares 180 F Ratios 182
Variance Estimates 182 Assumptions and Box s
Correction 183 Power 185 Comparisons
185 Treating Error as a Random Effect 187
Exercises 189
9 Other Incomplete Designs 196
Two Factor Designs —Incomplete Blocks 198
Balanced Incomplete Blocks 199
Three Factor Designs 206 Youden Squares 206
Latin Squares 209 Repeated Balanced Incomplete
Blocks 210
Higher way Designs 214
Exercises 216
10 One way Designs with Quantitative
Factors 220
Trend Analysis of One way Fixed Effects 221 The
Model Equation 221 Linear Trend 223 Higher
Order Trends 225
One Observation Per Cell 234 Trend Test 235
Estimating Trends 238
Contents ix
Random Effects Model — Correlation 238 Linear
Trend 239 Linear Correlation 242 Estimation
243 Other Tests, Power, Confidence Intervals, 245
Exercises 246
11 Trend Analyses in Multifactor Designs 248
Main Effects 248
Two way Interactions with One Numerical Factor 250
Significance Tests 250 Estimation 252
Higher way Interactions with One Numerical Factor
255 Significance Tests 259 Estimation 260
General Principles 262
Two Numerical Factors 265 Two way Interactions
265 Three way Interactions with Two Numerical
Factors 271
More than Two Numerical Factors 276 Three way
Interactions 277 Higher way Interactions 279
Factors with Unequally Spaced Numerical Values 282
Exercises 283
12 Multifactor Designs with Random
Numerical Factors 285
Two way Designs 285 The Model 286
Estimates of Effects 287 Significance Tests 289
Interpretation of Significance Tests 290
Assumptions 295 Linearity 295 Equal Slopes
295
Alternatives to the Analysis of Covariance 297
Experimental Control of the Covariate 297 Other
Kinds of Statistical Control 298
General Analysis of Covariance —Fixed Effects 299
The Model Equation 300 Estimates of Effects 300
Significance Tests 303 Testing for Equal Slopes
304
Random and Mixed Designs 305
Adjusted Grand Mean 307
Multiple Covariates 308
Relaxing the Assumptions 309
Exercises 309
x Contents
Appendix 313
Table A 1. Upper tail significance levels of the
standard normal distribution.
Table A 2. Values of the standard normal distribution
for selected two tailed significance levels.
Table A 3. Values of the chi square distribution for
selected one tailed significance levels.
Table A 4. Values of the t distribution for selected
two tailed significance levels.
Table A 5. Values of the F distribution for selected one
tailed significance levels.
Table A 6. Upper a point of Studentized range, for
a = 0.01, a = 0.05, and a = 0.10.
Table A 7. Coefficients of orthogonal polynomials.
Table A 8. Arcsin transformation (Z = 2 arcsin R).
Table A 9. Inverse arcsin transformation (Z to R).
Table A 10. Curves of constant power for selected
numerator degrees of freedom, v.
List of Symbols 330
Bibliography 335
Index 343
|
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| dewey-search | 519.5/35 |
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| dewey-tens | 510 - Mathematics |
| discipline | Psychologie Mathematik Wirtschaftswissenschaften |
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| indexdate | 2024-07-09T15:38:19Z |
| institution | BVB |
| isbn | 0716707748 |
| language | English |
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| physical | X, 352 S. graph. Darst. |
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| spelling | Lindman, Harold R. Verfasser aut Analysis of variance in complex experimental designs Harold R. Lindman San Francisco, Calif. Freeman 1974 X, 352 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse de variance Experimenteel ontwerp gtt Plan d'expérience Variantieanalyse gtt Analysis of variance Experimental design Versuchsplanung (DE-588)4078859-3 gnd rswk-swf Varianzanalyse (DE-588)4187413-4 gnd rswk-swf Varianzanalyse (DE-588)4187413-4 s DE-604 Versuchsplanung (DE-588)4078859-3 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001292111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lindman, Harold R. Analysis of variance in complex experimental designs Analyse de variance Experimenteel ontwerp gtt Plan d'expérience Variantieanalyse gtt Analysis of variance Experimental design Versuchsplanung (DE-588)4078859-3 gnd Varianzanalyse (DE-588)4187413-4 gnd |
| subject_GND | (DE-588)4078859-3 (DE-588)4187413-4 |
| title | Analysis of variance in complex experimental designs |
| title_auth | Analysis of variance in complex experimental designs |
| title_exact_search | Analysis of variance in complex experimental designs |
| title_full | Analysis of variance in complex experimental designs Harold R. Lindman |
| title_fullStr | Analysis of variance in complex experimental designs Harold R. Lindman |
| title_full_unstemmed | Analysis of variance in complex experimental designs Harold R. Lindman |
| title_short | Analysis of variance in complex experimental designs |
| title_sort | analysis of variance in complex experimental designs |
| topic | Analyse de variance Experimenteel ontwerp gtt Plan d'expérience Variantieanalyse gtt Analysis of variance Experimental design Versuchsplanung (DE-588)4078859-3 gnd Varianzanalyse (DE-588)4187413-4 gnd |
| topic_facet | Analyse de variance Experimenteel ontwerp Plan d'expérience Variantieanalyse Analysis of variance Experimental design Versuchsplanung Varianzanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001292111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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